"I go home alone."
Translation:나는 혼자 집에 갑니다.
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It seems so, yes. 저 as a pronoun is for socially lowering the speaker, while the -ㅂ니다 verb form raises the listener. So if the listener ranks lower than you socially (or in the workplace hierarchy), you could absolutely use -ㅂ니다 to raise them without using 저 to lower yourself (essentially signalling that you're closer to equals in the moment).
However, the Tips and Notes on the browser version notes that using 저 with -해요 verb endings "would be weird"; it's strange to lower yourself without also raising the listener (i.e. placing them above you in the social moment).
Tl;dr - you can use 나 with -ㅂ니다 but not 저 with -해요.